What is the tension in the cable of an elevator cab that weighs 27.0 kN when the cab's speed is (a) increasing at a rate of 1.07 m/s² and (b) decreasing at a rate of 1.07 m/s²?
Tension Calculation When Speed is Increasing
The tension in the cable when the cab's speed is increasing at a rate of 1.07 m/s² is 30,008.24 N.
To calculate the tension in the cable when the cab's speed is increasing, we first need to determine the mass of the elevator cab. Using the weight of the cab, w = 27.0 kN, and the acceleration, a = 1.07 m/s², we can find the mass, m.
Given:
Weight of elevator cab, w = 27,000 N
Acceleration, a = 1.07 m/s²
We can calculate the mass, m:
m = w/g
m = 27,000 N / 9.81 m/s²
m = 2,749.23 kg
Next, we use the formula T = w + ma to find the tension in the cable:
T = w + ma
T = 27,000 N + 2,749.23 kg × 1.07 m/s²
T = 30,008.24 N
Therefore, when the cab's speed is increasing at a rate of 1.07 m/s², the tension in the cable is 30,008.24 N.
Tension Calculation When Speed is Decreasing
The tension in the cable when the cab's speed is decreasing at a rate of 1.07 m/s² is 23,991.76 N.
To calculate the tension in the cable when the cab's speed is decreasing, we use a similar approach as above. The formula T = w - ma is used in this case.
T = w - ma
T = 27,000 N - 2,749.23 kg × 1.07 m/s²
T = 23,991.76 N
Therefore, when the cab's speed is decreasing at a rate of 1.07 m/s², the tension in the cable is 23,991.76 N.
In conclusion, the tension in the cable is 30,008.24 N when the cab's speed is increasing at a rate of 1.07 m/s², and it is 23,991.76 N when the cab's speed is decreasing at a rate of 1.07 m/s².